# IEEE 754 addition wrong result floating point numbers

I want to add two IEEE 754 numbers. I followed the steps to add two 754 numbers. However the result it not correct. Number 1: S:0 E:01111111 M:11111111111111111111111

Number 2: S:0 E:01111111 M:00000000000000000000000

Here is my calculation:

The site http://weitz.de/ieee/ gives this result: S: 0 E: 10000000 M: 10000000000000000000000

in my calculation the mantissa is 01111... Why?

• If you have more than 10 bits, it's very helpful to add a space between groups of four bits. Aug 14, 2020 at 8:04
• In their calculation I see the same mantissa as yours.
– plop
Aug 14, 2020 at 11:16
• What about number of bits & rounding? Aug 15, 2020 at 7:01
• Just rounding. Tere is one extra 1 on the right of the mantissa, with rounding 01111... becomes 10000..... Sep 13, 2020 at 9:17
• I’m voting to close this question because it is about one person making a mistake or misunderstanding something, and any answer would be completely useless for anyone else. Including OP who probably hasnt been stuck in this problem for three years. Jan 28 at 16:51

\begin{align}1&.01111111 \\+1&.11111111111111111111111\\=11&.01111110111111111111111\end{align}